Audrey Brooker
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Tasting Water
STAT 218
Do people prefer bottled water over tap water?
The observational units are the people tasting water.
The variable is t
Ashley marne, Travis Ferris, Aubrey, Garret
1.4 exploration competitive advantage to uniform colors?
1. the null hypothesis is that the players wearing red wont have any advantage over players wearing
blue. Alternative hypothesis is that the players weari
Full name:
UNL ID:
Anh P. Le
24064626
HOMEWORK 1 STAT870
1. 2.8.1
n = 18
t/2, n-2 = t0.25, 16 = 1.98
Scatter plot for linear regression model of the gross box office results for the current week vs.
previous week:
(a) 95% confidence interval for the slope
1.2 Measuring the Strength of Evidence
Binary variable: categorical variable with only 2
outcomes (e.g. gender, results of a coin flip, team win
or lose)
Symbols
is the long run proportion (parameter)
o e.g.
=
1
3
is the long run proportion of winning
at
3.1 and 3.4 Confidence Intervals
Example: Kissing Right?
A study showed that 80 out of 124 couples leaned their heads to
the right while kissing. Is the direction couples lean in actually
random?
H 0 : =0.50
H A : 0.50
^p=
p
80
=0.65
124
-value
0.0012
In
2.1: Sampling from a Finite Population
Review
Population: entire collect of observational units
Sample: subset of population
Parameter: numerical summary from population
(unknown)
Statistic: numerical summary from sample (known)
Definitions
Represent
1.3 Alternative Measure of Strength of Evidence
Example: Heart Transplant Operations
15% of patients who received heart transplant operations
nationally have died. After 8 out of 10 people who
received a heart transplant operation at St. Georges died,
res
1.4 What Impacts Strength of Evidence
z=
statistichypothesized value
standard error
1. Difference between the statistic and hypothesized
value
Further away the statistic is from the hypothesized
value => z-score gets bigger (in absolute value) =>
smaller
Name:_Key_ Score:_/50
STAT 218-014 Exam 1
Part 1: Multiple Choice (2 pts each). Select the best possible answer to each of the following questions.
1. A researcher wants to know if undergraduate students at UNL spend more than 10 hours a week
on homework.
2.2 Inference for One Mean
Definitions
Median: middle value in the data
o If the data follows a symmetric, normal
distribution, then median is close to the mean
e.g. 9, 5, 7, 2, 8
=> 2, 5, 7, 8, 9 (median = 7)
e.g. 9, 5, 7, 2, 8, 90
7 +8
=> 2, 5, 7, 8, 9
2.3 Errors and Significance
Type I error: Reject the null hypothesis when the null
hypothesis is true
Type II error: Fail to reject the null hypothesis when the
null hypothesis is false
Reality
H0
Reject
H0
Decision
Fail to reject
H0
is true
H0
is false
T
1.5 Inference using Theory-Based Approach
Theory-Based Approach (i.e. Normal Approximation)
Used to predict what the distribution will look like
under the null hypothesis
o Follows the bell-shaped curve
o Centered at parameter value
Central Limit Theor
Worksheet Chapter 02
To estimate the typical amount of TV watched per day by students at her school of 1000 students, a
student has all the students in her statistics class (30 students) take a short survey, finding that, on
average, students in her stati
Worksheet Chapter 02
To estimate the typical amount of TV watched per day by students at her school of 1000 students, a
student has all the students in her statistics class (30 students) take a short survey, finding that, on
average, students in her stati
Worksheet Chapter 01
1. An Austrian study was completed to determine if untrained sea lions and sea lionesses could
follow various experimenter-given cues when given a choice of two objects. One experimentergiven cue was to point at one of the objects. On
Name: _ Group: _
Quiz 02
In the latest Gallup survey, they asked a random sample of adult Americans if they had a gun in
their home. Of the 100 they surveyed 43 reported they did have a gun in their home. Describe
what each of the following are for this s
Parameter and One-Sided or Two-Sided hypothesis?
For each scenario below, identify: (1) the parameter of interest (in words) and (2) the hypotheses (in
words and symbols) corresponding to the research question. When determining hypotheses, pay special
att
Worksheet 01
Name:
Group No.:
1) For each of the research questions, identify the observational units and variable
of interest and which are quantitative, and which are categorical.
a) An instructor wants to investigate whether the color of paper (blue or
Final Review:
The final review data set contains data from a study to test whether exercising while trying to memorize information
was helpful. Students collected data by having individuals do jumping jacks while 10 words were read to them. They
recorded
Worksheet Chapter 04
In your own, think of a topic (may be based on your area of major)! After youve found a topic,
come up with a research question. Be creative! Then identify the following:
Observational units:
Explanatory variable:
Response variable:
C
Mathematical Statistics (NYU, Spring 2003)
Summary (answers to his potential exam questions)
By Rebecca Sela
1
Sucient statistic theorem (1)
Let X1 , ., Xn be a sample from the distribution f (x, ). Let T (X1 , ., Xn ) be
a sucient statistic for with cont
Statistics II (Discrete Methods: STAT 453/653) Fall 2007
Homework 5 Example Solution
Written by: Fares Qeadan, Reviewed by: Ilya Zaliapin
Department of Mathematics and Statistics, University of Nevada, Reno
Problem 5.1
Recall that a distribution f (x; ),
ECE 830 Fall 2011 Statistical Signal Processing
instructor: R. Nowak
Lecture 4: Sufficient Statistics
Consider a random variable X whose distribution p is parametrized by where is a scalar or a
vector. Denote this distribution as pX (x|) or p(x|), for sho
STAT 463
Spring, 2017
Homework 8
due Tuesday, 18 April 2017
1. Since previous studies have reported that elite athletes are often deficient in their nutritional intake (e.g.,
total calories, carbohydrates, protein), a group of researchers decided to evalu
STAT 463
Spring, 2017
Homework 5
due Tuesday, 28 February 2017
1. Let X1 , . . . , Xn be independent random variables with pdfs
ix
e
fXi (x; ) =
0
x i
x < i
On Homework 4, you showed that T = mini (Xi /i) is a sufficient statistics for . Explain why this
STAT 463
Spring, 2017
Homework 2
due Tuesday, 24 January 2017
1. On Homework 1, you worked with a random sample of size n from a distribution with pdf
1/x2 1 x < 1
f (x) =
0
else
Assuming that n is an odd number, find the pdf of the sample median.
2. Let
STAT 463
Spring, 2017
Homework 6
due Tuesday, 7 March 2017
1. We are interested in estimating the average number of tattoos that UNL students have. We randomly select
76 UNL students, and ask them how many tattoos they have. The total number of tattoos am
STAT 463
Spring, 2017
Homework 7
due Tuesday, 11 April 2017
1. Let X1 , . . . , Xn be iid uniform(0, ) random variables.
(a) Derive the LRT of H0 : = 0 versus Ha : 6= 0 . Find the exact critical value for a size test.
(b) Derive the power function for the
STAT 463
Spring, 2017
Homework 3
due Thursday, 2 February 2017
1. Find the maximum likelihood estimator (MLE) of based on a random sample X1 , . . . , Xn from each of the
following distributions
(a) f (x; ) = (1 )x1 , x = 1, 2, . . . ; 0 1
(b) f (x; ) = (
STAT 463
Spring, 2017
Homework 4
due Tuesday, 21 February 2017
1. Consider a random sample X1 , . . . , Xn from a uniform(1 , 2 ) distribution. We are interested in estimating the
2
mean of the uniform(1 , 2 ) distribution, = 1 +
2 .
(a) Two different est